Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 10y

Key Concepts

Objective Function

An objective function is a mathematical expression that defines the goal of an optimization problem, typically in terms of maximizing or minimizing a certain quantity. In this case, the objective function is given as 10y, indicating that the goal is to find the highest and lowest values of this function based on the constraints of the feasible region.

Feasible Region

The feasible region is the set of all possible points that satisfy the constraints of an optimization problem. It is typically represented graphically, and the maximum and minimum values of the objective function are found at the vertices or edges of this region. Understanding the shape and boundaries of the feasible region is crucial for determining where to evaluate the objective function.

Linear Programming

Linear programming is a method used to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. It involves optimizing an objective function subject to linear constraints. In this context, the problem requires applying linear programming techniques to find the maximum and minimum values of the objective function within the defined feasible region.